Solve (x-1)(x+6)-(x-2)(x-3)=3

$$( x - 1 ) ( x + 6 ) - ( x - 2 ) ( x - 3 ) = 3$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by x+6 and combine like terms.

$$x^{2}+5x-6-\left(x-2\right)\left(x-3\right)=3$$

Use the distributive property to multiply x-2 by x-3 and combine like terms.

$$x^{2}+5x-6-\left(x^{2}-5x+6\right)=3$$

To find the opposite of x^{2}-5x+6, find the opposite of each term.

$$x^{2}+5x-6-x^{2}+5x-6=3$$

Combine x^{2} and -x^{2} to get 0.

$$5x-6+5x-6=3$$

Combine 5x and 5x to get 10x.

$$10x-6-6=3$$

Subtract 6 from -6 to get -12.

$$10x-12=3$$

Add 12 to both sides.

$$10x=3+12$$

Add 3 and 12 to get 15.

$$10x=15$$

Divide both sides by 10.

$$x=\frac{15}{10}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{3}{2}$$